Simplification of the Local Two-Particle Vertex in DMFT

Dynamical Mean Field Theory (DMFT) is one of the most successful methods for studying strongly correlated systems. However, evaluating the local two-particle vertex̶—which is crucial in computing experimentally relevant correlation functions and serves as a key ingredient for considering the nonlocal correlation beyond the single-site DMFT —remains computationally demanding. To address this issue, we propose a simplification scheme for the local two-particle full-vertex. By focusing on the correspondence between the frequency and diagrammatic structures, we propose a simplified form of the local full-vertex that qualitatively reproduces the essential frequency structures of the exact full-vertex[1,2]. We validated the accuracy of the proposed scheme by comparison with the numerically exact continuous-time Monte Carlo method. In this presentation, we explain the details of the method and show the results of the benchmarks.

Reference

[1] R. M, M. Ochi, and K. Kuroki: J. Phys. Soc. Jpn. 91, 034002 (2022).

[2] R. M, K. Kuroki, and M. Ochi: Phys. Rev. B. 111, 205136 (2025).